The serial number list in Blue Book says the Stevens Model 38 was built from 1936-1945, and that there were 33,500 of them. Utility bolt action single - well, value is going to depend on condition, of course, but won't be high. I'd guess, in NRA Very Good or better, MAYBE $100-125. On a good day.

Given the fact that most civilian arms production essentially terminated once the US was in the war, it was most likely built soemtime between 1936 and 1942.